1. Field of the Invention
The present invention relates to a rotational angle measurement apparatus including a magneto-resistance element (MR element) having a pinned magnetic layer. The invention particularly relates to a rotational angle measurement apparatus capable of correcting a pin-angle error.
2. Description of the Related Art
A rotational angle measurement apparatus using such an MR element is known, for example, by Japanese Patent No. 3799270, etc.
Examples of known magneto-resistance elements (MR element) include a giant magneto-resistance element (GMR element) and a tunneling magneto-resistance element (TMR element). The outline of MR element is to be described by way of a magnetic field measurement apparatus using a GMR element as an example.
FIG. 1 shows a basic structure of the GMR element.
The GMR element has a first magnetic layer 13 (pinned magnetic layer) and a second magnetic layer 11 (free magnetic layer) in which a non-magnetic layer 12 (spacer layer) is sandwiched between both of the magnetic layers. When an external magnetic field is applied to the GMR element, while the magnetization direction of the pinned magnetic layer does not change and remains fixed as it is, the magnetization direction 20 of the free magnetic layer changes in accordance with the direction of the external magnetic field.
The angle of magnetization direction in the pinned magnetic layer is referred to as a pin angle and represented by θp.
When a voltage is applied across the end of the GMR element, a current flows in accordance with the resistance of the element, and the magnitude of the resistance of the element changes depending on the difference: Δθ=θf−θp between the magnetization direction (pin angle) θp of the pinned magnetic layer and the magnetization direction θf the free magnetic layer. Accordingly, when the magnetization direction θp of the pinned magnetic layer is known, the magnetization direction θf the free magnetic layer, that is, the direction of the external magnetic field can be detected by measuring the resistance value of the GMR element with the use of the property described above.
The mechanism in which the resistance value of the GMR element changes according to Δθ=θf−θp is as described below.
The magnetization direction in the thin-film magnetic film is concerned with the direction of electrons' spin in a magnetic material. Accordingly, in the case where Δθ=0, for the electrons in the free magnetic layer and the electrons in the pinned magnetic layer, the ratio of electrons with the directions of spins being identical is high. By contrast, in the case where Δθ=180°, the ratio of electrons with the directions of the spins opposite to each other is high for the electrons in both of the magnetic layers.
FIG. 2 schematically shows a cross section of the free magnetic layer 11, the spacer layer 12, and the pinned magnetic layer 13. Arrows shown in the free magnetic layer 11 and the pinned magnetic layer 13 schematically show the direction of the spin for majority electrons.
FIG. 2A shows a case where Δθ=0 in which the directions of spins are aligned in the free magnetic layer 11 and the pinned magnetic layer 13. FIG. 2B shows a case where Δθ=180° in which the directions of spins are opposite to each other in the free magnetic layer 11 and the pinned magnetic layer 13.
In the case of θ=0 in FIG. 2A, since electrons of an identical spin direction are predominant in the free magnetic layer 11, the right spin electrons emitting from the pinned magnetic layer 13 are less scattered in the free magnetic layer 11 and pass along the trajectory as an electron trajectory 810.
On the other hand, in the case of Δθ=180° in FIG. 2B, electrons of right spin emitting from the pinned magnetic layer 13 are scattered more frequently and pass along the trajectory as an electron trajectory 810 when entering the free magnetic layer 11, since there are many electrons of opposite spin. As described above, in the case where Δθ=180°, since electrons are scattered more frequently, electric resistance is increased.
In an intermediate case where AO is in the range between 0 and 180°, it is in an intermediate state between FIG. 2A and FIG. 2B. The resistance value R of the GMR element is represented as:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          1                ]                                                            R        =                                            R              0              ′                        +                                          G                2                            ⁢                              (                                  1                  -                                      cos                    ⁢                                                                                  ⁢                    Δ                    ⁢                                                                                  ⁢                    θ                                                  )                                              =                                    R              0                        -                                          G                2                            ⁢              cos              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              θ                                                          (        1        )            in which G/R is referred to as a GMR coefficient which is from several % to several tens %.
Since way of current flow (that is, electric resistance) can be controlled depending on the direction of the electrons' spin, the GMR element is also referred to as a spin-valve device.
Further, in a magnetic film of thin film thickness (thin-film magnetic film), since the demagnetizing factor in the direction normal to the surface is extremely large, the magnetization vector cannot rise vertically in the normal direction (direction of film thickness) and lies in the plane. Since both of the free magnetic layer 11 and the pinned magnetic layer 13 constituting the GMR element are sufficiently thin, respective magnetization vectors lie in the in-plane direction.
FIG. 3A shows a case where a Wheatstone bridge 60A is formed by using four GMR elements R1 (51-1) to R4 (51-4). The bridge 60A is used as a magnetic sensor.
In this case, the magnetization direction in the pinned magnetic layer of the GMR element R1 (51-1) and R3 (51-3) is set as θp=0, and the magnetization direction in the pinned magnetic layer of the GMR element R2 (51-2) and R4 (51-4) is set as θp=180°. Since the magnetization direction θf in the free magnetic layer is determined by an external magnetic field, and the magnetization direction θf is identical for four GMR elements. Therefore, a relation: Δθ2=θf−θp2=θf−θp1−π=Δθ1+π is established. Since Δθ1 is based on θp=0, it is substituted as: Δθ1=θ. Accordingly, as can be seen from the equation (1), the GMR elements R1, R3 are each represented by:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          2                ]                                                                      R          n                =                              R                          n              ⁢                                                          ⁢              0                                -                                    G              2                        ⁢            cos            ⁢                                                  ⁢            θ                                              (        2        )            in which (n=1, 3), and the GMR elements R2, R4 are each represented by:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          3                ]                                                                      R          n                =                              R                          n              ⁢                                                          ⁢              0                                +                                    G              2                        ⁢            cos            ⁢                                                  ⁢            θ                                              (        3        )            in which (n=2, 4).
When an excitation voltage e0 is applied to a bridge 60A, a differential voltage Δv=V2−V1 between terminals V1 and V2 is represented by the following equation (4):
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          4                ]                                                                      Δ          ⁢                                          ⁢          v                =                                                                              R                  1                                ⁢                                  R                  3                                            -                                                R                  2                                ⁢                                  R                  4                                                                                    (                                                      R                    1                                    +                                      R                    4                                                  )                            ⁢                              (                                                      R                    2                                    +                                      R                    3                                                  )                                              ⁢                      e            0                                              (        4        )            When substituting the equation (2) and the equation (3) into the equation (4), assuming Rn0 as equal for n=1 to 4, and setting as: R0=Rn0, it is represented as:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          5                ]                                                                      Δ          ⁢                                          ⁢                      v            c                          =                                                            -                                  e                  0                                            ⁢              G              ⁢                                                          ⁢              cos              ⁢                                                          ⁢              θ                                      2              ⁢                                                          ⁢                              R                0                                              ≡                      -                          V              x                                                          (        5        )            
As described above, since the signal voltage Δv is in proportion to cos θ, the direction θ of the magnetic field can be detected. Further, since the bridge outputs a signal in proportion to cos θ, it is referred to as a COS bridge.
Further, FIG. 3B shows a bridge 60B in which the direction in the pinned magnetic layer is changed by 90° from that of the COS bridge in FIG. 3A. That is, the bridge is constructed with GMR elements at θp=90° and 270°. By calculating in the same manner as described above, we obtain the signal voltage as follows:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          6                ]                                                                      Δ          ⁢                                          ⁢                      v            s                          =                                                            e                0                            ⁢              G              ⁢                                                          ⁢              sin              ⁢                                                          ⁢              θ                                      2              ⁢                                                          ⁢                              R                0                                              ≡                      V            y                                              (        6        )            Since the signal voltage is in proportion to sin θ, the bridge 60B is referred to as a SIN bridge.
By calculating the arctangent for the ratio of two output signals of the COS bridge and the SIN bridge, the direction θm of the magnetic field vector (angle of magnetic field) is determined as:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          7                ]                                                                      Arc          ⁢                                          ⁢                      Tan            ⁡                          (                                                Δ                  ⁢                                                                          ⁢                                      v                    s                                                                                        -                    Δ                                    ⁢                                                                          ⁢                                      v                    c                                                              )                                      =                              Arc            ⁢                                                  ⁢                          Tan              ⁡                              (                                                      V                    y                                                        V                    x                                                  )                                              =                                    Arc              ⁢                                                          ⁢                              Tan                ⁡                                  (                                                            sin                      ⁢                                                                                          ⁢                      θ                                                              cos                      ⁢                                                                                          ⁢                      θ                                                        )                                                      =            θ                                              (        7        )            
As described above, the magneto-resistance element has a feature capable of directly detecting the direction of the magnetic field.
The magnetic field dependent term for the resistance of the magneto-resistance element is determined by the difference Δθ=θm−θp between the magnetization direction (pin angle) θp of the pinned magnetic layer and the angle of the external magnetic field θm as shown in the equation (1). In other words, the pin angle θp is a reference angle. Accordingly, when the setting for the pin angle includes an error, the equation (5) and the equation (6) are not valid and the angle determined according to the equation (7) no more shows an exact angle of magnetic field θm.
As an example, it is assumed that the pin angle of the GMR elements R2, R4 of the COS bridge shown in FIG. 3A is deviates by 0.5° from the respective correct angle, and the pin angle of the GMR elements R2, R4 of the SIN bridge shown in FIG. 3B deviates by −1°.
FIG. 4 shows a difference (i.e. measurement error) between the angle θ1 determined from signals Vx and Vy from each of the bridges in accordance with the equation (7) and a real angle of the magnetic field θm in the case described above. The measurement error changes depending on the real angle of magnetic field θm and has amplitude of about 1°. As described above, the pin-angle error of 1° corresponds to an angle measurement error of about 1°. Accordingly, in order to obtain measurement accuracy, for example, of ±0.2°, it is necessary to set all pin angles at an accuracy of about 0.2°.
A method of manufacturing a magnetic sensor having a plurality of pin angles therein includes, for example, a method of arranging magneto-resistance elements (corresponding to each of Ri (i=1 to 4) in FIG. 3) or a method of changing the direction of the external magnetic field applied upon depositing the pinned magnetic layer. However, in any of the methods, it is extremely difficult to set all pin angles each at a high accuracy of about 0.2°.
Concerning to this problem, a method of correcting an angle measurement error caused by the pin-angle error has been known (for example, refer to JP-2006-194861-A).
In JP-2006-194861-A, a rotational angle θ and a measurement angle θ(meas) measured by a magnetic sensor at this instance are measured, and then an error Δφ(θ) between both of them is determined as function of the rotational angle θ. That is, the error is represented as:[Equation 8]Δφ(θ)=θ(meas)−θ  (8)
Then, since the error Δφ(θ) is in the form of a 180° cycle as shown in FIG. 4, correction function S1 (θ, α) is defined as shown by the equation (9) as:
                    [                  Equation          ⁢                                                            ⁢                                                          ⁢          9                ]                                                                      S          ⁢                                          ⁢          1          ⁢                      (                          θ              ,              α                        )                          =                              α            2                    ⁢                      (                          1              +                              cos                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                θ                                      )                                              (        9        )            
Then, a parameter α is determined such that a function E1 (α) defined by the following equation (10) is minimum:[Equation 10]E1(α)=∫[Δφ(θ)−S1(θ,Δ)]2dθ  (10)where integration is a 1 cycle integration for θ=0 to 360°.
After the error of a second harmonic component is removed as described above, a fourth harmonic component is left. Then, the correction function S2(θ, β) for fourth harmonic is defined as shown in the following equation (11);[Equation 11]S2(θ,β)=−β sin 4θ  (11)
Then, a parameter β is determined such that a function E2 (β) defined by the following equation (12) is minimum:[Equation 12]E2(β)=∫[Δφ(θ)−S1(θ,α)−S2(θ,β)]2dθ  (12)
During operation of the magnetic sensor, the error is corrected by using the correction function determined as described above according to the following equation[Equation 13]θ(compensated)=θ(meas)−S1(θ,α)−S2(θ,β)  (13)